Details

analyze368.0ms (5.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
50%	50%	0.1%	5
62.4%	37.5%	0.1%	6
62.4%	37.5%	0.1%	7
68.7%	31.2%	0.1%	8
68.7%	31.2%	0.1%	9
71.8%	28.1%	0.1%	10
71.8%	28.1%	0.1%	11
73.4%	26.5%	0.1%	12
73.4%	26.5%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample3.3s (47.9%)

Results

1.8s	4019×	body	8192	exit
777.0ms	6763×	body	128	valid
359.0ms	3861×	body	128	invalid
186.0ms	737×	body	512	valid
124.0ms	741×	body	256	valid
4.0ms	15×	body	1024	valid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

568×	`neg-mul-1_binary64`
503×	`fma-def_binary64`
491×	`fma-neg_binary64`
484×	`div-sub_binary64`
416×	`distribute-neg-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	22	23
2	58	23
3	152	21
4	338	18
5	1090	18
6	2902	18
7	3695	18
8	4706	18
9	4881	18

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

11.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	11.5b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	14.3b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

Compiler

Compiled 94 to 48 computations (48.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (exp.f64 wj)) wj)
✓	0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
✓	0.0b	(/.f64 x (exp.f64 wj))
✓	1.9b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series62.0ms (0.9%)

Counts

4 → 61

Calls

4 calls:

21.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
16.0ms	(/.f64 x (exp.f64 wj))
15.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
10.0ms	(-.f64 (/.f64 x (exp.f64 wj)) wj)

rewrite64.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-sqr-sqrt_binary64`
95×	`*-un-lft-identity_binary64`
75×	`times-frac_binary64`
67×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`

Counts

4 → 171

Calls

4 calls:

17.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
17.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
8.0ms	(-.f64 (/.f64 x (exp.f64 wj)) wj)
3.0ms	(/.f64 x (exp.f64 wj))

simplify158.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1035×	`fma-neg_binary64`
613×	`times-frac_binary64`
411×	`distribute-rgt-in_binary64`
220×	`sub-neg_binary64`
180×	`fma-def_binary64`

Counts

232 → 240

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	296	4475
1	694	4262
2	2367	4057
3	4896	4050
4	5533	4050

prune156.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	237	3	240
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	238	4	242

Error

0.1b

Counts

242 → 4

Alt Table

Status	Error	Program
	38.0b	(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	11.5b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
▶	4.8b	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))
	37.2b	(exp.f64 (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))

Compiler

Compiled 5635 to 2105 computations (62.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))
✓	0.0b	(fma.f64 5/2 (.f64 wj wj) (.f64 wj -2))
✓	0.0b	(.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2)))

series39.0ms (0.6%)

Counts

3 → 60

Calls

3 calls:

18.0ms	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))
18.0ms	(.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2)))
3.0ms	(fma.f64 5/2 (.f64 wj wj) (.f64 wj -2))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`fma-udef_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 51

Calls

3 calls:

3.0ms	(.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2)))
3.0ms	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))
0.0ms	(fma.f64 5/2 (.f64 wj wj) (.f64 wj -2))

simplify94.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

766×	`fma-neg_binary64`
474×	`fma-def_binary64`
393×	`associate-l_binary64`
371×	`distribute-rgt-in_binary64`
350×	`associate-r_binary64`

Counts

111 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	1943
1	246	1662
2	774	1456
3	3401	1456
4	4684	1456
5	4952	1456

prune86.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	110	4	114

Error

0.1b

Counts

114 → 4

Alt Table

Status	Error	Program
	38.0b	(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	11.5b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	4.8b	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))
▶	37.2b	(exp.f64 (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))

Compiler

Compiled 2276 to 1134 computations (50.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (exp.f64 wj))
✓	1.2b	(log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
	1.9b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	2.2b	(exp.f64 (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))

series134.0ms (1.9%)

Counts

2 → 48

Calls

2 calls:

113.0ms	(log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
21.0ms	(exp.f64 (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
8×	`log-prod_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-sum_binary64`

Counts

2 → 37

Calls

2 calls:

18.0ms	(exp.f64 (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))
16.0ms	(log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

simplify108.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

384×	`associate-+r+_binary64`
319×	`times-frac_binary64`
288×	`+-commutative_binary64`
262×	`associate-/l*_binary64`
246×	`associate-+l+_binary64`

Counts

85 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	4478
1	1043	4135
2	4809	4134
3	4973	4134

prune171.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	190	2	192
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	192	4	196

Error

0.1b

Counts

196 → 4

Alt Table

Status	Error	Program
▶	37.7b	(exp.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))))
✓	4.8b	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))
	49.6b	(exp.f64 (log.f64 (fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))
✓	11.5b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Compiler

Compiled 7105 to 4031 computations (43.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(cbrt.f64 (.f64 (.f64 (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))))
	1.2b	(log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
	1.9b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	2.2b	(exp.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))))

series136.0ms (2%)

Counts

2 → 48

Calls

2 calls:

114.0ms

(cbrt.f64 (*.f64 (*.f64 (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))))

21.0ms

(exp.f64 (cbrt.f64 (*.f64 (*.f64 (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`exp-prod_binary64`
3×	`add-log-exp_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 26

Calls

2 calls:

3.0ms

(cbrt.f64 (*.f64 (*.f64 (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))))

2.0ms

(exp.f64 (cbrt.f64 (*.f64 (*.f64 (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))))

simplify165.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

384×	`associate-+r+_binary64`
319×	`times-frac_binary64`
282×	`+-commutative_binary64`
259×	`associate-/l*_binary64`
245×	`associate-+l+_binary64`

Counts

74 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	294	5208
1	995	3891
2	4656	3673
3	4984	3673
4	4976	3673

prune616.0ms (8.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	425	2	427
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	426	5	431

Error

0.1b

Counts

431 → 5

Alt Table

Status	Error	Program
	52.1b	(exp.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (log.f64 (log1p.f64 (expm1.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))))))
	38.2b	(exp.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (log.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))) (log.f64 (fma.f64 (*.f64 (cbrt.f64 wj) (cbrt.f64 wj)) (cbrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))))
✓	4.8b	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))
	49.6b	(exp.f64 (log.f64 (fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))))
✓	11.5b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Compiler

Compiled 31047 to 16847 computations (45.7% saved)

regimes919.0ms (13.2%)

Accuracy

Total 0.1b remaining (16.8%)

Threshold costs 0.1b (16.8%)

Counts

138 → 3

Compiler

Compiled 12726 to 7311 computations (42.6% saved)

bsearch35.0ms (0.5%)

Steps

Iters	Range		Point
8	3.1819851040301035e-16	7.943667249242625e-12	7.73535415808421e-12
7	-0.0001005179086298632	-1.2797078716861815e-6	-1.3031958808623259e-6

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	69
1	38	69
2	42	69
3	44	69
4	45	69
5	44	69

end126.0ms (1.8%)

Compiler: Compiled 246 to 139 computations (43.5% saved)

Details

analyze368.0ms (5.3%)

sample3.3s (47.9%)

simplify79.0ms (1.1%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series62.0ms (0.9%)

rewrite64.0ms (0.9%)

simplify158.0ms (2.3%)

prune156.0ms (2.3%)

localize10.0ms (0.1%)

series39.0ms (0.6%)

rewrite10.0ms (0.1%)

simplify94.0ms (1.4%)

prune86.0ms (1.2%)

localize10.0ms (0.1%)

series134.0ms (1.9%)

rewrite37.0ms (0.5%)

simplify108.0ms (1.6%)

prune171.0ms (2.5%)

localize14.0ms (0.2%)

series136.0ms (2%)

rewrite8.0ms (0.1%)

simplify165.0ms (2.4%)

prune616.0ms (8.9%)

regimes919.0ms (13.2%)

bsearch35.0ms (0.5%)

simplify4.0ms (0.1%)

end126.0ms (1.8%)

Profiling